how far did they travel going to Grandma’s and what was their average speed on the trip there?

Question

Jack and Jill took a trip to Grandma’s house. It took them 8 hr to get to Grandma’s house but on their way back home they took the scenic route, which is 20 mi longer. If their speed going home was 10 mi/hr less than their speed going to Grandma’s house, and if it took them 10 hr to get home

Answer 1

Let s be the distance to Grandma’s and v the speed they went to get to Grandma’s.

So s=8v, because it took them 8 hours to get there.

Coming back they travelled s+20 miles. Since s=8v we can write this as 8v+20 miles.

Their speed was reduced by 10mph so that’s v-10. It took them 10 hours to return so:

8v+20=10(v-10); 8v+20=10v-100; 120=2v so v=60mph. This is their average speed going to Grandma’s.